few_shots: Example:
Problem/activity:
Problem 1
The table below contains single equations in a single variable, single equations in two variables, and pairs of simultaneous equations in two variables. Check the appropriate box to show whether there is no solution, exactly 1 solution, or if there is an infinite number of solutions.
|                                                          | **           No solution          ** | **           Exactly 1 solution          ** | **           Infinite number of solutions          ** |
|----------------------------------------------------------|--------------------------------------|---------------------------------------------|-------------------------------------------------------|
|                       $${9=4x+7}$$                       |                                      |                                             |                                                       |
|                       $${y=3y+5}$$                       |                                      |                                             |                                                       |
|                    $${y={x\over2}}$$                     |                                      |                                             |                                                       |
|                     $${3x+6y-9=0}$$                      |                                      |                                             |                                                       |
|    $${x=y}$$                        $${1.25x=1.25y}$$    |                                      |                                             |                                                       |
| $${9.9=6x+8y}$$                        $${9x=2.5y-8.8}$$ |                                      |                                             |                                                       |
| $${11x-2y=1.5}$$                        $${11x-2y=2.5}$$ |                                      |                                             |                                                       |
Problem 2
Kim has a small container and a large container as shown.
[IMG]
It takes 16 of the small containers to fill the large container. Three small containers leave 1.95 gallons of space in the big container.
What is the size of each of the two containers?


Standard options: 
A. Solve linear equations in one variable.
B. Analyze and solve pairs of simultaneous linear equations.


Thought: The last three rows of the table in the first problem involves solving pairs of simultaneous linear equations. The second word problem can also be represented as two simultaneous linear equations.
Answer: B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_001392

8
options: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.

Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
problem_activity: Narrative
This activity prompts students to compare multiple fractions and put them in order by size. The work gives students opportunities to look for and make use of structure (MP7) in each set of fractions and make comparisons strategically. For instance, rather than comparing two fractions at a time and in the order they are listed, students could first classify the given fractions as greater or less than
\(\frac{1}{2}\)
or 1, look for fractions with a common numerator or denominator, and so on.
If time is limited, consider asking students to choose two sets of fractions to compare and order.
Representation: Internalize Comprehension.
Synthesis: Invite students to identify which details were most useful when putting fractions in order. Display the sentence frame, “The next time I put fractions in order, I will pay attention to . . . .”
Supports accessibility for: Memory
Launch
Groups of 2
Activity
“Work independently on two sets. Then, discuss your work with your partner and complete the rest together.”
10 minutes: independent work time
Monitor for students who look for and make use of structure. Ask them to share during lesson synthesis.
3–4 minutes: partner discussion
Student Facing
Put each set of fractions in order, from least to greatest. Be prepared to explain your reasoning.
\(\frac{3}{12} \qquad \frac{2}{4} \qquad \frac{2}{3} \qquad \frac{1}{8}\)
\(\frac{8}{5} \qquad \frac{5}{6} \qquad \frac{11}{12} \qquad \frac{11}{10}\)
\(\frac{21}{20} \qquad \frac{9}{10} \qquad \frac{6}{5} \qquad \frac{101}{100}\)
\(\frac{5}{8} \qquad \frac{2}{5} \qquad \frac{3}{7} \qquad \frac{3}{6}\)
Student Response
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Advancing Student Thinking
Some students may try to write equivalent fractions with a common denominator for all four fractions in each set before comparing them but may be unable to do so. Encourage them to try reasoning about two fractions at a time, and to use what they know about the fractions to determine how they compare (to one another or to familiar benchmarks).
Activity Synthesis
See lesson synthesis.


correct_option_index: 0